Is an IP address specific to each PC or the home?
There are two types of IP address - public and private. Your public one is used by the router to connect to the Internet. Each device that's connected to your router has a different private address.
I have deleted my temporary internet files and browsing history and cookies but it still shows my name on the website,............
Either you haven't deleted your temporary Internet files and cookies properly, or you're using a favourite/bookmark to access that site and its URL contains a unique identifier.